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Momentum

Momentum. Momentum. A measure of how hard it is to stop a moving object. Related to both mass and velocity. Possessed by all moving objects. Calculating Momentum. For one particle p = m v For a system of multiple particles P =  p i =  m i v i Momentum is a vector!.

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Momentum

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  1. Momentum

  2. Momentum • A measure of how hard it is to stop a moving object. • Related to both mass and velocity. • Possessed by all moving objects.

  3. Calculating Momentum • For one particle p = mv • For a system of multiple particles P = pi = mivi • Momentum is a vector!

  4. Which has the most momentum?

  5. Impulse (J) The product of an external force and time, which results in a change in momentum J = F t J = p • Units: N•s or kg•m/s

  6. Impulse (J) F(N) 3000 2000 area under curve 1000 0 t (ms) 0 1 2 3 4

  7. Law of Conservation of Momentum If the resultant external force on a system is zero, then the vector sum of the momenta of the objects will remain constant. pi= pf

  8. Collisions • Collisions are governed by Newton's laws. • Newton’s Third Law tells us that the force exerted by body A on body B in a collision is equal and opposite to the force exerted by body B on body A.

  9. Collisions • During a collision, external forces are ignored. • The time frame of the collision is very short. • The forces are impulsive forces (high force, short duration).

  10. Collision Types • Elastic (hard, no deformation) • p is conserved, KE is conserved • Inelastic (soft; deformation) • p is conserved, KE is NOT conserved • Perfectly Inelastic (stick together) • p is conserved, KE is NOT conserved

  11. Inelastic Collisions • Only momentum is conserved. • Kinetic Energy is not conserved. • Some deformation of the object(s) will occur. • Perfectly inelastic collision is when the objects actually “stick” together. • Examples are: automobile crashes, catching a ball, recoil of a gun.

  12. Perfectly Inelastic Collision #1 An 80 kg roller skating grandma collides inelastically with a 40 kg kid as shown. What is their velocity after the collision?

  13. Perfectly Inelastic Collisions #2 A train of mass 4M moving 5 km/hr couples with a flatcar of mass M at rest. What is the velocity of the cars after they couple?

  14. Perfectly Inelastic Collisions #3 A 1.14-kg skateboard is coasting along the pavement at a speed of 3.53 m/s, when a 1.1-kg cat drops from a tree vertically down on the skateboard. What is the speed of the skateboard-cat combination?

  15. Explosions and Recoil • When an object separates suddenly, this is the reverse of a perfectly inelastic collision. • Mathematically, it is handled just like an ordinary inelastic collision. • Momentum is conserved, kinetic energy is not. • Examples: • Cannons, Guns, Explosions, Radioactive decay.

  16. Recoil Problem #1 A gun recoils when it is fired. The recoil is the result of action-reaction force pairs. Calculate the Recoil velocity Mass of Gun = 2.1 kg Mass of Man= 75 kg Mass of Bullet = 0.001 Kg Muzzle Velocity = 450 m/s

  17. Elastic Collisions • Momentum and Kinetic Energy are conserved. • No deformation of objects occurs. • Examples are: billiard balls (pool), particle collisions, marbles.

  18. Elastic Collision #1 • A 7-g marble has a head-on collision with a 3-g marble, initially at rest on a playing surface. The speed of the 7-g marble is reduced from 1.08 m/s to 0.75 m/s in the collision. What is the speed of 3-g marble after the collision?

  19. Elastic Collision #2 • A 4-gram object moving to the right with a speed of 3.9 cm/s makes an elastic head-on collision with a 6-gram object moving in the opposite direction with a speed of 6.6 cm/s. Find the velocities after the collision.

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